The answer to this is a general 'no.' Especially since you say 'reliably' - swords in any form are not armour-piercing weapons.

As I say in previous answer

Regarding the use of swords in battle, it is true that a sword cannot penetrate plate armour. It also has difficulty penetrating mail armour (it can't penetrate with a slash, and likely will fail to penetrate with a thrust) Alan Williams showed that mail+some padding can resist more force than swords can easily deliver, at least with slashes) and fabric armour like cloth jacks (which can resist slashing blows far stronger than those delivered by any sword). In general, swords are not armour-penetrating weapons. This is the result of simple physics - sword slashes distribute the force of their blows along the length of the blade that strikes the target, while thrusts concentrate force at the point. And swords can thrust, which is part of what makes them so flexible. As early as the 13th century men at arms are instructed to thrust through mail and the weaker points or gaps in armour. However for sheer force a two-handed thrusting weapon like an ahlspiesse would be more useful, or the even the point of a less-single-purpose polearm like a pollaxe, bill or halberd. Also much more powerful were the backspikes of polearms and warhammers, which concentrated all the force created by the leverage of a swing into a single point - these were important enough that some weapons, such as the 'bec de faucon' were named after their backspike, not the 'front' of their head. I will say nothing of maces (which you already mentioned) and lances and crossbows and guns. These are all weapons that are much more effective at smashing or piercing armour than swords are.)

Penetrating plate armour requires efficiently transferring large amounts of force to a narrow area of the armour. To do this, you need to strike with significant force (which is hard, sword thrusts don't produce the forces of lance strikes or axe-blows because they have no leverage and little mass behind them) at a right angle against a curved (moving!) surface. The thinnest parts of plate armour (the arms/gauntlets) are the parts that are both most acutely curved and the most likely to be in motion. This means that efficient force transfer is very difficult, and things like helmet skulls and breastplate fronts are very thick! So even in cases where a sword thrust might pierce a comparably thick metal plate, doing it in combat is a different story.

We see the evidence for this in the way in which people fought in armour, which we can see in contemporary fencing manuals. They did not swing or thrust away for maximum force, but instead held their swords in a grip halfway up the blade. This provides fine point control to find the gaps of armour - the back sides of elbows, armpits, visor eyeslits, opened visors, the packs of knees, groins, even the gaps of articulation in between plates. It is far better to go around armour than through it. The technique of thrusting into the gaps of armour is also attested in battle as early as the mid-13th century (the very beginning of supplementing mail with plate). As Allan Williams relates in The Knight and the Blast Furnace:

Oman, quoting the crhoniclers, describes how this [supplemental plate armour] rendered them invulnerable to the swords of the French until the Germans raised their arms to strike, when they exposed the opening [under their arms]. The cry ran down the ranks of the French knights, who were numerically superior but being pushed back, "give point" and the French started to stab them under the arm...

Taken in this context, the acute points of Oakshott's types XV, XVI, XVII and XVIII can be seen in a different light - as aids not to thrusting -through- plate armour, but into its gaps, possibly using their stiff plates to pry their way in.

Now, a word about Oakshott. His name looms large in the history of studying swords, because he did a lot to describe the development of sword blades so expertly. His insights into swords forms are considerable, and by placing swords into the context in which they were used he helped change the way we talk about them as objects. That said, he was not a trained historian, and he began writing when the modern study of arms and armour was still new. He did consult with some imminent authorities in the field (like the great Claude Blair, whom everyone consulted with) but sometimes he uses sources incautiously to provide evidence for his preferred interpretation. This is one of these cases, I think. Sources need to be read critically - they aren't necessarily simple accounts of 'what really happened' but have all sorts of purposes, from entertainment to edification to propaganda. Without looking at the original source, I'm not sure of how close it is to the original event, and why it relates things the way it does. Perhaps it is drawing from a literary tradition of gore and excessive armour penetration in romances (that goes back to Virgil and ultimately Homer), perhaps it was written by someone years after the event who was not there. Individual incidents in the Middle Ages need to be taken in the larger context of what we know was and wasn't possible, bringing together the evidence of fighting techniques, materials science and surviving artifacts.